在线性平等限制及其统计估计下,所有最小方格问题及其统计估计的结构化条件数 (Structured condition numbers for the total least squares problem with linear equality constraint and their statistical estimation)

from arxiv, There are servals reasons. 1) I need to add some new results in section 3 for unstructured condition number. 2) need to add new authors list. 3) we want to add more numerical example to show our results efficient and take less time. 4) We want to add the comparison in section 4

In this paper, we derive the mixed and componentwise condition numbers for a linear function of the solution to the total least squares with linear equality constraint (TLSE) problem. The explicit expressions of the mixed and componentwise condition numbers by dual techniques under both unstructured and structured componentwise perturbations is considered. With the intermediate result, i.e. we can recover the both unstructured and structured condition number for the TLS problem. We choose the small-sample statistical condition estimation method to estimate both unstructured and structured condition numbers with high reliability. Numerical experiments are provided to illustrate the obtained results.

翻译：在本文中,我们得出了具有线性平等制约(TLSE)问题的总最小方的解决方案的线性函数的混合和成份条件数字。在未结构化和结构化的组件扰动下,考虑了以两用技术提供的混合和成份条件数字的明确表达。中间结果,即我们可以为TLS问题恢复无结构化和结构化条件数字。我们选择了小型抽样统计条件估计方法,以非常可靠地估计非结构化和结构化条件数字。提供了数字实验,以说明所获得的结果。